The Ghana international arrived at the San Siro on an 18-month deal as a free transfer following his nine-year stint with Chelsea.
Essien is Seeforf's first acquisition since taking charge of the Rossoneri a fortnight ago, and the Netherlands legend concedes that he cannot wait to begin working with the stalwart.
He told the club's official website: "I know him very well. He's a great player, a warrior I can use in the midfield.
"He will give also bring big values on and off the pitch. He's a guy with personality that will be useful for the team."
The 31-year-old was the Blues' record signing upon arriving at Stamford Bridge from Lyon in 2005 for a fee in the region of £24m.